1. Field of the Invention.
The present invention relates generally to adaptive matched filters and more particularly to adaptive matched filters which adapt the filter characteristic based on the noise power spectral density.
2. Description of the Related Art.
There are many systems which must process or detect a signal of known spectral content which is in the presence of background noise. Such systems may include communication systems, infrared detection systems, radar systems, and video systems, or the like. If the system is operating at a very low signal-to-noise ratio, the known signal is usually embedded in the noise. The problem at hand is to first determine if the known signal is present in the noise, and then having found this signal, provide an output signal which has an enhanced signal-to-noise ratio.
A common approach to this problem is to use a filter which maximizes the ratio of peak signal to the noise power at one instant in time. Such a filter is termed a matched filter. Generally, this filter is specifically designed for a given background noise and a given signal of known amplitude-time history. The desired filter characteristic may be determined by utilizing Fourier analysis techniques.
For example, if the input signal x(t) to the matched filter is comprised of a signal s(t) and an additive noise signal n(t), which may be expressed as x(t)=s(t)+n(t), then the matched filter characteristic is determined as provided hereinbelow. Defining S(.omega.) as the Fourier transform of s(t), and assuming that the noise signal has zero mean and power spectral density P(.omega.), the output of a filter with transfer function H(.omega.) may be described as ##EQU1##
In these equations y.sub.s (t) is the output component at the matched filter output due to the signal s(t) and W is the output power due to the noise n(t). Maximizing the ratio of the peak signal to the noise power results in EQU H(.omega.)=S*(.omega.)/P(.omega.) (3)
where S*(.omega.) is the complex conjugate of S(.omega.). A fixed mechanization of this filter will only be optimum for signal and noise characteristics used in determining H(.omega.). In the time domain, H(.omega.) corresponds to the linear causal time-invariant filter whose impulse response h(t) is the inverse Fourier transform of H(.omega.). In the above equations, the use of "t" indicates signals in the continuous time domain, and the use of ".omega." indicates signals in the frequency domain.
Because the above-described filter is only optimal for specified signal and noise characteristics, it has no flexibility. Accordingly, numerous devices have been invented which attempt to provide some flexibility to the matched filter, and hence provide an adaptive matched filter. For example, in U.S. Pat. No. 3,889,108 an "Adaptive Low Pass Filter" is disclosed which adaptively changes its bandwidth filtering characteristics in accordance with the bandwidth of the incoming signal. This adaptive filer is designed to pass low-frequency components below a selected low-frequency cutoff point. The filter cutoff point may be increased to a higher frequency or decreased to a lower frequency by utilizing prior signal inputs and outputs of the filter. U.S. Pat. No. 4,038,539, for "Adaptive Pulse Processing Means and Method", provides for a digital system which generates a filter function based on the frequency characteristics of the input signal.
U.S. Pat. No. 4,034,199, for a "Programmable Analog Transversal Filter", discloses a filter which provides for a programmable finite impulse response. A plurality of filter taps are provided which allow an applied signal to be variably weighted in accordance with a program. This system permits the implementation of complex signal processing with particular implementation of Fourier transforms, matched filters, correlators, and adaptive type filters, by selecting the proper control program.
U.S. Pat. No. 4,044,241, for an "Adaptive Matched Digital Filter," provides for a digital filter which is of the transversal type, whose multiplier coefficients are controlled and periodically updated by a digital computer. The computer samples the incoming noise and signal at frequent intervals in order to monitor any changes in the noise environment. The computer calculates and sets optimum filter constants for a given noise environment.
U.S. Pat. No. 3,303,335, entitled "Digital Correlation System Having an Adjustable Impulse Generator", provides for a digital filtering system wherein the synthesizing of the desired input response is carried out directly in the time domain through automatic and repeated evaluation of the convolution integral.
Although numerous adaptive matched filters have been designed, no such filters have attempted to adapt the filter characteristic as a function of the noise power spectral density for a given form of signal. Hence, it would be an improvement in the electronic filtering art to provide for an adaptive matched filter which adapts the filter characteristic as a function of the noise power spectral density.